Chapter 20, Problem 17SE

Many factors influence the retail price of computers. The table below shows the average retail price for a computer, including both desktops and laptops, during the month of November for each of the indicated years (Wall Street Journal, December 13, 2010).

Year	Average Price ($)
2007	795
2008	705
2009	580
2010	615

1. a. Use 2007 as the base year and develop a price index for the retail price of a computer over this four-year period.
2. b. Use 2008 as the base year and develop a price index for the retail price of a computer over this four-year period.

To determine

Find the price index for the retail price of a computer over the four-year period by using 2007 as the base year.

Answer to Problem 17SE

The price index for the retail price of a computer over the four-year period by using 2007 as the base year is,

Year	Average Price ($)	$\text{Price relative in Period }t$
2007	795	100
2008	705	88.679
2009	580	72.956
2010	615	77.3585

Explanation of Solution

Calculation:

The data represents the values of average retail price for a computer in the month of November for each year from 2007 to 2010.

The price index for the retail price of a computer over the four-year period by using 2007 as the base year is obtained below:

Year	Average Price ($)	$\text{Price relative in Period }t=\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)$
2007	795	$\frac{795}{795}\left(100\right)=100$
2008	705	$\frac{705}{795}\left(100\right)=88.679$
2009	580	$\frac{580}{795}\left(100\right)=72.956$
2010	615	$\frac{615}{795}\left(100\right)=77.3585$

To determine

Find the price index for the retail price of a computer over the four-year period by using 2008 as the base year.

Answer to Problem 17SE

The price index for the retail price of a computer over the four-year period by using 2008 as the base year is,

Year	Average Price ($)	$\text{Price relative in Period }t$
2007	795	112.766
2008	705	100
2009	580	82.2695
2010	615	87.234

Explanation of Solution

Calculation:

The price index for the retail price of a computer over the four-year period by using 2008 as the base year is obtained below:

Year	Average Price ($)	$\text{Price relative in Period }t=\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)$
2007	795	$\frac{795}{705}\left(100\right)=112.766$
2008	705	$\frac{705}{705}\left(100\right)=100$
2009	580	$\frac{580}{705}\left(100\right)=82.2695$
2010	615	$\frac{615}{705}\left(100\right)=87.234$